1. Field of the Invention
The present invention relates to a method for interpolative extension of a nuclear magnetic resonance image obtained by an imaging system utilizing a phenomenon of nuclear magnetic resonance (NMR).
2. Description of the Prior Art
A nuclear magnetic resonance image (hereinafter referred to as MR image) is formed of two-dimensional position data based on a nuclear magnetic resonance signal (hereinafter referred to as NMR signal) which is produced by utilizing a phenomenon of nuclear magnetic resonance and represents the spin density, relaxation time or related information of specific atomic nuclei existing in a test piece. FIG. 2 shows an exemplary pulse sequence for obtaining an NMR signal disclosed in British Patent Specification No. 2,079,946; and FIG. 3 shows the procedure of producing an MR image from an NMR signal, in which (a) is a flow chart of a conventional method for interpolative extension of the MR image, and (b) typically illustrates the process in the flow chart correspondingly to the individual steps thereof.
Detailed descriptions on the NMR imaging have already been known in various books and papers (e.g. Edelstein W. A. et al., "Physics of Medical Biology" 25: 751 (1980); NMR Medical Study Society (ed.), "NMR Medicine", Maruzen). Therefore, an explanation will be given here principally on how to produce an image from the NMR signal obtained in the pulse sequence of FIG. 2.
In FIG. 2, Gx and Gy represent a phase-encoding magnetic field and a frequency-encoding magnetic field, respectively. Suppose now that, for explanation, an NMR signal is obtained by systematically changing Gx M times (normally M is so selected as to be a power of 2, such as 128 or 256). Referring to FIG. 3 (b) which typically illustrates the process executed in (a), the NMR signal phase-encoded by the first magnetic field Gx is digitized by A-D conversion M times during the sampling period shown in FIG. 2, and the data is inserted into an array of (1, my) where my=1, 2, 3, . . . , M. Similarly, the signal encoded by the next magnetic field Gx is inserted into (2, my). And finally by the Mth magnetic field Gx changed systematically, there is obtained a two-dimensional array (mx, my) where mx=1, 2, . . . , M; and my=1, 2, . . . , M, in which the NMR signal is existent [step 1]. The array (mx, my) is then changed by two-dimensional Fourier transformation of M.times.M [step 2], and if the two-dimensional array of complex thus obtained is $ (kx, ky) where kx=1, 2, . . . , M and ky=1, 2, . . . , M, a two-dimensional array F having an absolute value $ expressed as F (kx, ky)=.vertline.$ (kx, ky).vertline. becomes an MR image of M.times.M pixels [step 3]. And N.times.N pixels (e.g. in double extension where N=2.times.M) are processed by linear interpolation to achieve extension [step 4], thereby forming a two-dimensional array G (lx, ly) where lx=1, 2, . . . , N and ly=1, 2, . . . , N which represents the image. In this case, the image G extended by linear interpolation is obtained from the array F in the following manner: ##EQU1##
And the image G of N x N pixels extended by linear interpolation is displayed [step 5].
However, in the conventional method for interpolative extension of an MR image, first an image is once formed as mentioned above and then is extended on its planar space by linear interpolation, so that due to the principle of such linear interpolation, some problems are unavoidable including that the image after interpolative extension becomes indistinct to eventually bring about a reduction in the resolution.